Continuous unsaturated second-order hybrid multi-stable stochastic energy resonance and its application in rolling bearing fault diagnosis

Abstract

Stochastic resonance (SR) is highly favored for early mechanical fault signal extraction because it enhances weak features using external noise. However, traditional SR models suffer from output saturation. In this paper, a novel second-order hybrid multi-stable stochastic resonance (SHMSR) system is developed, where the sigmoid function is first employed to construct a continuous unsaturated multi-stable potential function. Then, system performance is theoretically evaluated by the steady-state probability density function under different external forces based on adiabatic approximation theory. Furthermore, the input energy is used as an index to measure the influence of system internal parameters on SR performance, which not only simplifies the metrics of stochastic processes in complex systems but also explains the physical nature of parameter-induced SR. Finally, an adaptive weak signal detection method is proposed to demonstrate the superiority of the novel system in practical engineering. Simulations and experiments with different noise conditions, rotational speeds and fault characteristics regarding the detection and enhancement of weak bearing fault signals under strong background noise are conducted to evaluate the adaptability and robustness of the novel method. The results demonstrate that SHMSR can effectively improving the signal-to-noise ratio (SNR) and amplifying the amplitude of the feature signal in early mechanical fault signal extraction.